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1. Which of the following is the equation of a circle with center (a, −b) and radius r?

A. (x−a)2+(y+b)2=r2

B. (x+a)2+(y−b)2=r2

C. (x+a)2+(y−b)2=r

D. (x−a)2+(y+b)2=r

2. A given circle has the equation x2+y2−4x−2y+4=1. What is the center of the circle?
A. (1, 2)

B. (−2, −1)

C. (−1, −2)

D. (2, 1)

User Miguel Ortiz
by
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1 Answer

23 votes
23 votes

Answer:

1) A

2) D

Explanation:

1) The equation of a circle is (x-h)²+(y-k)²=r² where (h,k) is the center and "r" is the radius of the circle. With a center of (a,-b) the equation of the circle is (x-a)²+(y+b)²=r² making A the correct answer.

2) Convert from general form into standard form:

Given: x²+y²-4x-2y+4=1

Rearrange: x²-4x+4+y²-2y=1

Set right side equal to 0: x²-4x+4+y²-2y-1=0

Complete the square: x²-4x+4+y²-2y-1+2=0+2

Evaluate: x²-4x+4+y²-2y+1=2

Condense: (x-2)²+(y-1)²=2

Therefore, the center of the circle is D) (2,1)

User Alex Beardsley
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2.6k points